Question

Add subtract factor and expand expressions quick check

Answer 1

Certainly! Here’s a quick overview of how to add, subtract, and expand expressions, followed by a few examples for practice.

### Adding and Subtracting Expressions

1. **Combine Like Terms**: Identify terms that have the same variable and exponent.
2. **Simple Addition**: Add the coefficients of like terms.
3. **Simple Subtraction**: Subtract the coefficients of like terms.

### Expanding Expressions

1. **Distributive Property**: Use \(a(b+c) = ab + ac\).
2. **FOIL Method for Binomials**: For two binomials \( (a + b)(c + d) \):
- First: \(ac\)
- Outside: \(ad\)
- Inside: \(bc\)
- Last: \(bd\)
- Combine all results: \(ac + ad + bc + bd\)

### Examples

#### 1. Adding Expressions
**Example**: Add \(3x + 4y + 2x - y\).

**Solution**:
- Combine like terms: \( (3x + 2x) + (4y - y) = 5x + 3y \).

#### 2. Subtracting Expressions
**Example**: Subtract \(2x + 3y\) from \(5x - y\).

**Solution**:
- Distribute the negative: \(5x - y - (2x + 3y) = 5x - y - 2x - 3y\).
- Combine like terms: \( (5x - 2x) + (-y - 3y) = 3x - 4y \).

#### 3. Expanding Expressions
**Example**: Expand \( (x + 2)(x + 3) \).

**Solution**:
Using the FOIL method:
- First: \(x \cdot x = x^2\)
- Outside: \(x \cdot 3 = 3x\)
- Inside: \(2 \cdot x = 2x\)
- Last: \(2 \cdot 3 = 6\)

Combine: \( x^2 + 3x + 2x + 6 = x^2 + 5x + 6 \).

### Quick Check Practice Problems

1. Add: \(2a + 5b + 3a - 2b\).
2. Subtract: \(4m - 3n - (2m + n)\).
3. Expand: \( (2x + 1)(x + 4) \).

### Solutions to Practice Problems
1. \( (2a + 3a) + (5b - 2b) = 5a + 3b \)
2. \( (4m - 2m) + (-3n - n) = 2m - 4n \)
3. \( (2x \cdot x + 2x \cdot 4 + 1 \cdot x + 1 \cdot 4) = 2x^2 + 8x + x + 4 = 2x^2 + 9x + 4 \)

Feel free to ask if you need more examples or clarifications!